Least Common Multiple (LCM) of 54 and 57
The least common multiple (LCM) of 54 and 57 is 1026.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 54 and 57?
First, calculate the GCD of 54 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 57 = 0 remainder 54 |
| 2 | 57 ÷ 54 = 1 remainder 3 |
| 3 | 54 ÷ 3 = 18 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 140 | 1120 |
| 148 and 180 | 6660 |
| 166 and 27 | 4482 |
| 18 and 30 | 90 |
| 181 and 77 | 13937 |